I realize you know most of this TexasBama, but adding detail for others.
I had previously just scanned the image of the building layout previously posted. In looking at it a little more and thinking back about that report makes me think more about just simply rusted out reinforcement on the beams could be it too. In concrete beams, you have 2 types of reinforcing. You have longitudinal steel that that takes the tension component due to bending. The bottom steel does the work between columns, the top steel over the top of the column. You also have stirrups. These are closed ties in a rectangular shape that are oriented vertically in the beam. Basically, they encase the long bars. They resist shear. Concrete takes part of the shear, the stirrups take the rest. You space them closer than half the depth of the beam. If you draw a 45 degree line on an edge view of the beam, you space these strirrups so that they always cross the 45 degree line. If not, a crack is not being crossed by steel, which is bad.
Stirrups are normally smaller bars, #3-#5. For #8 and below, you take the bar size and divide it by 8 for the diameter. A #4 bar is 0.5" in diameter. The longitudinal bars are typically bigger bars, #8 and above. They'd take longer to rust. So, if you're having all of those water issues and your stirrups have significantly deteriorated, you could have a sudden shear failure on a beam. When that happens, you likely still have a decent amount of longitudinal steel in good enough shape to do work/be intact. This means that the failing beam could yank on the rest of the assembly and then start a domino effect.
This leads to the question about it just suddenly and randomly happening. Concrete is heavy. A parking deck is only designed for 50 psf live load (future traffic). That plaza would have been designed for either 100psf, or, more likely, a firetruck. Firetrucks are darn heavy, but we'll ignore that for this example. Say those columns are on a 25' grid. This is just an example to illustrate the weight and is a gross oversimplification in many ways. 25*25*50psf = 31250# = 31.25k. Say you had a 6" slab, 14"x20" joists @ 8'-4" and then say a 48"x20" girder. The slab weighs 75psf. The joists about 25psf. The beam would be about 28psf. This estimate is a little high because there is some double counting on the beam and joist occupying the same space. Still, you're looking about 128psf - a little, but still 25*25*128 = 80k. Let's say the design live load was 100psf instead of 50, that means it's 62.5k. Your total would be 142.5k. 80/142.5 = .561, meaning over half the load is actually there. Adding weight for pavers, etc, puts you probably at 60% or more of the total design load actually in place. You're not allowed for the concrete to take over half the shear. If the shear steel had significantly rusted out, then you have over half the total design load in place and only concrete there to take the load, but you don't want the concrete to ever take over half the load. I'm not saying this is what happens, but it passes the initial smell test.